mixed integer linear programming problem

Fuzzy multi-choice problems are widely used in the real world in the fields of industry, agriculture, science, technology, etc. Therefore, studying and solving such problems is essential. This study introduces some methods to solve fully fuzzy multi-choice linear programming problems.

To solve the fully fuzzy multi-choice linear programming problems, we use the linear least squares polynomial to convert the multi-choice linear programming problem to a mixed integer linear programming problem. Also, we convert the problem from the fuzzy mode to the crisp mode by using the defuzzification methods (Roubens ranking function.

To investigate the efficiency of the suggested method, we solve and compare two fully fuzzy multi-choice linear programming models using the proposed methods. In general, the resulting algorithms are simple and very inexpensive to implement, and they are more efficient than those of previous studies.

In this article, all parameters and coefficients of the problem are triangular fuzzy numbers, and the right side of the problem's constraints are the fuzzy multi-choice parameters. The number of fuzzy multi-choice parameters in the previous articles has been considered only two fuzzy choices. However, in this article, the number of these parameters can be arbitrary. Also, this article uses the fuzzy linear least squares method to approximate the fuzzy multi-choice parameters.

Electric vehicles (EVs) are new and growing loads in distribution networks. Increasing number of electric vehicles in a distribution network causes increase of electricity energy demand. Therefore, in the absence of any energy consumption management, some distribution system operation constraints (e.g. bus voltage magnitude) may be violated. Power electronic devices used for charging and discharging the batteries, are usually called chargers. The charger could be unidirectional (transfer the energy from network to the battery) or bidirectional. Bidirectional chargers work in four areas of PQ power plane. In this paper, firstly, the active and reactive power management of smart distribution network using electric vehicles as non-linear problem is presented. Then, the problem is converted to mixed integer linear programming (MILP) problem using specific linearization method and is solved by GAMS package. The proposed scheme has been tested on the 33-bus distribution network and its performance and capability have been evaluated by simulation results.

Electric vehicles (EVs) are new and growing loads in distribution networks. Increasing number of electric vehicles in a distribution network causes increase of electricity energy demand. Therefore, in the absence of any energy consumption management, some distribution system operation constraints (e.g. bus voltage magnitude) may be violated. Power electronic devices used for charging and discharging the batteries, are usually called chargers. The charger could be unidirectional (transfer the energy from network to the battery) or bidirectional. Bidirectional chargers work in four areas of PQ power plane. In this paper, firstly, the active and reactive power management of smart distribution network using electric vehicles as non-linear problem is presented. Then, the problem is converted to mixed integer linear programming (MILP) problem using specific linearization method and is solved by GAMS package. The proposed scheme has been tested on the 33-bus distribution network and its performance and capability have been evaluated by simulation results.